Leren wrote:You don't have to know anything about how to solve Jigsaw puzzles and you don't need any special software, just a lot of patience, or determination !

Amen! Congratulations

Leren, have a cigar!! I am truly impressed.

What we actually have here are two Latin Squares with the property that each one acts as the jigsaw layout (aka GDL) for the other.

Thus all cells with the same

color in one puzzle will have the same

value in the other, and vice-versa. See the solution posted below.

This can only be done with pairs of Latin Squares that are

orthogonal. Two Latin Squares

L1, L2 are said to be orthogonal if every pair {

L1(r,c), L2(r,c)} is unique. For size 9x9 it seems that roughly 1% of LS's have an orthogonal pair.

The concept of orthogonality can be extended to include GDL's (jigsaw layouts) - thus solving a Sudoku is simply finding a Latin Square that is orthogonal to the given GDL. (see note below)

My idea is to produce pairs of puzzles like this, in which the jigsaw codes are also obscured, but there are just enough givens and jigsaw codes to complete the puzzle.

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PS: for those of you familiar with Knuth's

Dancing Links (DLX) algorithm, it's interesting to note that one of the exercises in Knuth Vol 4 (Section 7 - Combinatorial Searching, Exercise #17), asks how the problem of finding orthogonal pairs , for a given LS, can be expressed as an

exact cover problem. The answer is exactly what DLX Sudoku solvers work with.